Definition of the Magnetic Field

John W. Dooley, Physics Department, Millersville University

Based on our definition of the magnetic field due to polarization,

we can describe the net magnetic field in a region as being caused by two different effects:

1) The effect of distant magnets, such as the used above.

2) The effect of polarization, .

Then we can write for the observed field with the paramagnetic material present (the "full" field):

The second line uses our result relating to the dipole moment per unit volume. Because the field from distant magnets is indistinguishable from the field due to local polarization, it is traditional to make the two terms on the right hand side of the equation look alike. To do this, we define a new field:

so that

can be imagined to be a polarization (of the vacuum!) caused by distant electromagnets. This leaves the rather unnerving impression that the vacuum is not quite the featureless void that it is supposed to be. Unnerving or not, truth lies in this direction.

Definition of Magnetic Susceptibility,

For magnetic materials it is traditional to describe the relation between polarization and applied field in terms of instead of . Thus becomes

or, for isotropic materials,

where

The parameter is called the magnetic susceptibility. The susceptibility is a property of matter, like elastic constants, density, and dielectric constant. In practice it is measured for each kind of material and tabulated in handbooks. Since and have the same units, the susceptibility is dimensionless.

For paramagnetic materials, . Note that if then

tells us that the magnetic field due to polarization is just as large as the applied field which caused it. This would be a very strong response to an applied field.

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